Structures affines et projectives sur les surfaces complexes. (Affine and projective structures on complex surfaces) (Q1266221)

It is known by works of \textit{M. Inoue, S. Kobayashi} and \textit{T. Ochiai} [J. Fac. Sci. Univ. Tokyo, Sect. I A 27, 247-264 (1980; Zbl 0467.32014)] that admitting a holomorphic connection is biholomorphically to either a complex torus or a Kodaira's surface or a Hopf's affine surface or an Inoue's surface or a holomorphic principal fiber over a closed Riemann surface of genus greater or equal to two, with odd first Betti number. They prove that such a surface has a complex affine structure. The author proceeds to describe in a geometric way all complex affine surfaces and for each fixed one all such structures which are compatible with its analytic structure.